SUSHI: An algorithm for source separation of hyperspectralimages with non-stationary spectral variation. Semi-blind Unmixing with Sparsity for Hyperspectral Images

Abstract

Hyperspectral images are data cubes with two spatial dimensions and a third spectral dimension, providing a spectrum for each pixel, and thus allowing the mapping of extended sources' physical properties. In this article, we present the Semi-blind Unmixing with Sparsity for Hyperspectral Images (SUSHI), an algorithm for non-stationary unmixing of hyperspectral images with spatial regularization of spectral parameters. The method allows for the disentangling of physical components without the assumption of a unique spectrum for each component. Thus, unlike most source separation methods used in astrophysics, all physical components obtained by SUSHI vary in spectral shape and in amplitude across the data cube. Non-stationary source separation is an ill-posed inverse problem that needs to be constrained. We achieve this by training a spectral model and applying a spatial regularization constraint on its parameters. For the spectral model, we used an Interpolatory Auto-Encoder, a generative model that can be trained with limited samples. For spatial regularization, we applied a sparsity constraint on the wavelet transform of the model parameter maps. We applied SUSHI to a toy model meant to resemble supernova remnants in X-ray astrophysics, though the method may be used on any extended source with any hyperspectral instrument. We compared this result to the one obtained by a classic 1D fit on each individual pixel. We find that SUSHI obtains more accurate results, particularly when it comes to reconstructing physical parameters. We then applied SUSHI to real X-ray data from the supernova remnant Cassiopeia A and to the Crab Nebula. The results obtained are realistic and in accordance with past findings but have a much better spatial resolution. Thanks to spatial regularization, SUSHI can obtain reliable physical parameters at fine scales that are out of reach for pixel-by-pixel methods.